28630 - Control Systems T-A

Learning outcomes

Knowledge of methodological and operational tools for analysis and synthesis of linear dynamic systems, in open loop and in closed loop.

Course contents

PREREQUISITES

Since this is a fundamental course in Automatic Control, no specific prerequisites are required.

PROGRAM AND CONTENTS

The course aims to provide basic knowledge for the analysis and synthesis of linear time-invariant control systems in both the time and frequency domains.

Fundamentals: systems; oriented systems; systems with zero initial conditions; algebraic and dynamic mathematical models; linearity and time-invariance; block diagrams and their reduction rules; open-loop and closed-loop control systems.

Analysis of linear time-invariant dynamical systems: linear ordinary differential equations with constant coefficients; solution of homogeneous differential equations with nonzero-initial conditions; solution of forced differential equations with zero initial conditions; solution of forced differential equations with nonzero initial conditions; the Laplace transform; conditions for a function of time to be L-transformable; the theorem of convergence; linearity of the Laplace transform; theorems on the Laplace transform; application of the Laplace transform to the solution of linear differential equations; the transfer function of linear systems; inverse Laplace transform by partial-fraction expansion: simple poles and multiple-order poles; modes; canonical responses; Dirac impulse; convolution integral; step response of first order systems (settling time); step response of second order systems (damping ratio and natural frequency, overshoot and settling time).

Frequency-domain analysis: frequency response; theorem of sinusoidal steady-state response; impulse response and frequency response; Bode plots; asymptotic Bode plots of first and second order terms; construction of Bode plots by composition of elementary terms; resonant peak and resonant frequency of the prototype second-order system; polar plots (Nyquist plots) and their asymptotic behavior.

Stability of feedback control systems: asymptotic stability; Routh-Hurwitz criterion; special cases when Routh's tabulation terminates prematurely; evaluation of the marginal value of a system parameter for system stability by means of the Routh-Hurwitz criterion; sensitivity of feedback control systems (parameter variations, disturbances, bandwidth); steady-state error of feedback control systems (unit and non-unit feedback gain); Nyquist criterion (systems with and without poles in the right-half complex plane); conditionally stable systems; stability margins and their representation in Nyquist and Bode plots; time-delay systems: stability analysis by the Nyquist criterion.

The root-locus design method: a perspective on the root-locus design method; guidelines for sketching a root locus; center of mass theore of the root locus; extension of the root-locus method.

Control systems design: design specifications, controller configurations, fundamental principles of design; cascade compensation networks: phase-lead network, phase-lag network, lead-lag network, bridged-T network; inversion formulas for the phase-lead network with DC gain preservation; design of phase-lead compensators by inversion formulas and Bode diagrams; design of phase-lag compensators by inversion formulas and Bode diagrams; design of phase-lead compensators by pole-zero cancellation; design of lead-lag compensators by Bode diagrams; design of bridged-T compensators by pole-zero cancellation; PID controllers and their tuning; design of PID controllers by Bode diagrams; design of PID controllers by pole-zero cancellation; Ziegler and Nichols' step response and frequency response methods.

Readings/Bibliography

E. Zattoni, "Controlli automatici: raccolta di prove scritte con soluzione" in G. Marro, "Controlli automatici", 5a ed. con cd-rom, Zanichelli, Bologna, 2006.

http://online.universita.zanichelli.it/marro/files/2015/05/prove_risolte.pdf

E. Zattoni, "Controlli automatici: raccolta di esercitazioni risolte con TFI" in G. Marro, "Controlli automatici", 5a ed. con cd-rom, Zanichelli, Bologna, 2006.

http://online.universita.zanichelli.it/marro/files/2015/05/esercitazioni.pdf

G. Marro, "Controlli automatici", 5a ed. con cd-rom, Zanichelli, Bologna, 2006.

G. F. Franklin, J. D. Powell, A. Emami-Naeini, "Feedback Control of Dynamic Systems: 5th Edition", Pearson-Prentice Hall, Upper Saddle River, NJ, 2006.

R. C. Dorf, R. H. Bishop, "Modern Control Systems: 10th Edition", Pearson-Prentice Hall, Upper Saddle River, NJ, 2005.

F. Golnaraghi and B. C. Kuo, "Automatic Control Systems: 9th Edition", John Wiley & Sons, Hoboken, NJ, 2010.

K. Ogata, "Modern Control Engineering", Pearson Education, Upper Saddle River, NJ, 2010.

L. Qiu and K. Zhou, "Introduction to Feedback Control", Pearson Education, Upper Saddle River, NJ, 2010.

Teaching methods

Lectures: Thorough treatment of methodological aspects

Exercises: Discussion of worked-out exercises and solved problems, including those supported by computer-aided tools for control system design.

Assessment methods

The final exam consists of a written test normally comprising 15 exercises covering topics from the entire course. The exam aims to assess the achievement of the following learning objectives:

• In-depth knowledge of the fundamental tools for the analysis and synthesis of linear time-invariant control systems;

• Ability to analyze the main properties of linear time-invariant dynamical systems;

• Knowledge of the primary methodologies for the synthesis of feedback control systems in both the time and the frequency domains.

The dates of the written tests are scheduled according to the academic calendar and communicated via the Almaesami service. There are six exam sittings per academic year: three in the summer session (the first available after the course ends), one in the autumn session, and two in the winter session. Registration for the exam is carried out solely and exclusively through the Almaesami service, within the designated registration period.

Students with Specific Learning Disabilities (SLD) or temporary or permanent disabilities are advised to contact the university office responsible well in advance (https://site.unibo.it/studenti-con-disabilita-e-dsa/it ). The office will propose any necessary accommodations to the students, which must in any case be submitted at least 15 days in advance for approval by the course chair, who will evaluate their suitability in relation to the educational objectives of the course.

Teaching tools

Computer-Assisted Exercises: Presented in class and to be carried out independently by students, these exercises focus on the computer-aided design of single-input single output feedback control systems. In particular, the use of TFI (Transfer Function Interpreter), which is a collection of Matlab programs, enables easy manipulation of transfer functions and provides access to the main mathematical and graphical procedures for the study of control systems.

Office hours

See the website of Elena Zattoni